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We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves iteratively a sequence of auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from…

Optimization and Control · Mathematics 2020-08-24 Yoni Choukroun , Michael Zibulevsky , Pavel Kisilev

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

Optimization and Control · Mathematics 2021-06-15 Vladislav Tominin , Yaroslav Tominin , Ekaterina Borodich , Dmitry Kovalev , Alexander Gasnikov , Pavel Dvurechensky

One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…

Data Structures and Algorithms · Computer Science 2014-05-22 Aharon Ben-Tal , Arkadi Nemirovski

We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…

Machine Learning · Computer Science 2024-06-10 Gergely Neu , Nneka Okolo

We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs…

Optimization and Control · Mathematics 2025-10-14 Chuan He , Zhaosong Lu

In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…

Optimization and Control · Mathematics 2015-11-16 Cong Dang , Guanghui Lan

We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…

Machine Learning · Computer Science 2019-09-17 Luo Luo , Cheng Chen , Yujun Li , Guangzeng Xie , Zhihua Zhang

We provide a simple and generic adaptive restart scheme for convex optimization that is able to achieve worst-case bounds matching (up to constant multiplicative factors) optimal restart schemes that require knowledge of problem specific…

Optimization and Control · Mathematics 2020-08-18 Oliver Hinder , Miles Lubin

In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…

Optimization and Control · Mathematics 2019-10-10 Andrei Kulunchakov , Julien Mairal

We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the…

Optimization and Control · Mathematics 2023-07-25 Le Thi Khanh Hien , Renbo Zhao , William B. Haskell

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

Optimization and Control · Mathematics 2020-06-23 Pascal Bianchi , Walid Hachem , Adil Salim

We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…

Optimization and Control · Mathematics 2019-11-28 Darina Dvinskikh , Eduard Gorbunov , Alexander Gasnikov , Pavel Dvurechensky , Cesar A. Uribe

Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…

Optimization and Control · Mathematics 2021-09-07 Abdurakhmon Sadiev , Aleksandr Beznosikov , Pavel Dvurechensky , Alexander Gasnikov

In this paper, we study a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. While restart strategies…

Optimization and Control · Mathematics 2026-02-05 Xinming Wu , Zi Xu , Huiling Zhang

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…

Optimization and Control · Mathematics 2022-11-15 Killian Wood , Emiliano Dall'Anese

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However,…

Optimization and Control · Mathematics 2017-03-09 Jialei Wang , Lin Xiao

Large-scale saddle-point problems arise in such machine learning tasks as GANs and linear models with affine constraints. In this paper, we study distributed saddle-point problems (SPP) with strongly-convex-strongly-concave smooth…

Optimization and Control · Mathematics 2022-10-04 Dmitriy Metelev , Alexander Rogozin , Alexander Gasnikov , Dmitry Kovalev

This paper presents a proximal-point-based catalyst scheme for simple first-order methods applied to convex minimization and convex-concave minimax problems. In particular, for smooth and (strongly)-convex minimization problems, the…

Optimization and Control · Mathematics 2023-11-09 Guanghui Lan , Yan Li

We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…

Optimization and Control · Mathematics 2016-02-26 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…

Optimization and Control · Mathematics 2022-02-15 Mohammad Alkousa , Alexander Gasnikov , Pavel Dvurechensky , Abdurakhmon Sadiev , Lama Razouk